Cellularity of Some Semigroup Algebras
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- 作者：Yingdan Ji ; Yanfeng Luo
- 关键词：Cellular algebras ; Semigroup algebras ; Rees matrix semigroups ; U ; semiabundant semigroups ; Monoid algebras
- 刊名：Bulletin of the Malaysian Mathematical Sciences Society
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：40
- 期：1
- 页码：215-235
- 全文大小：
- 刊物类别：Mathematics, general; Applications of Mathematics;
- 刊物主题：Mathematics, general; Applications of Mathematics;
- 出版者：Springer Singapore
- ISSN：2180-4206
- 卷排序：40
文摘
In this paper, we study the cellularity of some semigroup algebras. We show that the semigroup algebra of a U-semiabundant semigroup with Rees matrix semigroups over monoids as its principal \(\sim _U\)-factors is a cellular algebra if and only if all of the monoid algebras are cellular. We also study the cellularity of the semigroup algebra of a semilattice of Rees matrix semigroups. As consequences, we get the cellularity of super abundant semigroup algebras and complete regular semigroup algebras.